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kolbaska11 [484]
3 years ago
5

The photography club decides to publish a calendar to raise money. The initial cost is 600$. In addition to the initial cost eac

h calendar cost 2.50 to produce. The club plans to sell the calendars for 8$ each. Write and solve an inequality to find the number of calendars that the photography club must sell in order to raise at least 1200$
Mathematics
1 answer:
velikii [3]3 years ago
4 0

Answer:

110 calendars to have a profit of atleast 1200.

Step-by-step explanation:

Initial expense = 600

Let the number of calendars that the photography club must sell in order to raise at least 1200$ be x.

Cost per calendar = 2.5

Cost for x calendars = 2.5 x

Total expenses = 2.5 x + 600

Income per calendar = 8

Income = 8 x

Minimum profit = 1200

Therefore the inequality is,

8x - 2.5 x + 600 ≥ 1200

Solving we get,

5.5x ≥ 600

x ≥ 109.09

x ≥ 110

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Answer:

There is strong evidence that less than 87% of the orders are delivered in less than 10 minutes.

Decision rule: Reject the null hypothesis if (P-value < level of significance)

Test statistic z=-2.70

Decision: Reject the null hypothesis (0.003<0.010)

Step-by-step explanation:

In this question we have to test an hypothesis.

The null and alternative hypothesis are:

H_0: \pi\geq0.87\\\\H_a:\pi

The significance level is assumed to be 0.01.

The sample of size n=80 gives a proportion of p=61/80=0.7625.

The standard deviation is:

\sigma=\sqrt{\frac{\pi(1-\pi)}{N} }=\sqrt{\frac{0.87*0.13}{80} }=0.0376

The statistic z is then

z=\frac{p-\pi+0.5/N}{\sigma}=\frac{0.7625-0.87+0.5/80}{0.0376} } =\frac{-10125}{0.0376} =-2.70

The P-value is

P(z

The P-value (0.003) is smaller than the significance level (0.010), so the effect is significant. The null hypothesis is rejected.

There is strong evidence that less than 87% of the orders are delivered in less than 10 minutes.

Decision rule: Reject the null hypothesis if (P-value < level of significance)

Test statistic z=-2.70

Decision: Reject the null hypothesis (0.003<0.010)

6 0
3 years ago
Rotate the vector (0,2) 270 degrees counterclockwise about the origin
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<h3>Answer:  (2,0)</h3>

Explanation:

The vector (0,2) points directly north and the length of this vector is 2 units. It's the distance from (0,0) to (0,2).

When rotating 270 degrees counterclockwise, we'll turn to the left or westward direction (90 degrees so far) then at some point aim directly south (180 degrees so far) and finally ultimately end up pointing directly east (after getting to 270). So that's how we go from (0,2) to (2,0).

If you were to go clockwise, then everything flips and you'll ultimately end up pointing directly west. The length of the vector stays the same the whole time.

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3 years ago
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Answer:

130 miles

Step-by-step explanation:

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the scale drawing is usually reduced at a constant dimension

scale of the drawing = original dimensions / dimensions of the scale drawing

Actual distance = 31/4 x 40

convert 31/4 to an improper fraction

to convert to improper fraction, take the following steps :  

1. Multiply the whole number  by the denominator

2. Add the numerator to the answer gotten in the previous step

3. divide the number gotten in the previous step by the denominator  

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